On a half-wavelength patch antenna, the current is maximum and the voltage is zero at the center of the patch. Hence, you can short the center of the patch.

The result: the current will flow down through the shorting pin instead of to the end of the patch. Hence, you can make your antenna half the size.

The gain of the antenna will decrease, because the radiation of the half-wave patch is due to fringing fields on both sides of the patch; by shorting the center you will eliminate one of these sets. Hence, the pattern will be less directional and therefore the gain will be lower.

The bandwidth of an antenna increases with its volume; antennas with a smaller volume generally have a smaller bandwidth. Since you're shorted antenna is effectively half the size as a half-wave patch, your bandwidth will decrease.